Question: Simplify the following expression: $ t = \dfrac{5y - 7}{-6} - \dfrac{-2}{3} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{5y - 7}{-6} \times \dfrac{3}{3} = \dfrac{15y - 21}{-18} $ Multiply the second expression by $\dfrac{-6}{-6}$ $ \dfrac{-2}{3} \times \dfrac{-6}{-6} = \dfrac{12}{-18} $ Therefore $ t = \dfrac{15y - 21}{-18} - \dfrac{12}{-18} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{15y - 21 - 12 }{-18} $ Distribute the negative sign: $t = \dfrac{15y - 21 - 12}{-18}$ $t = \dfrac{15y - 33}{-18}$ Simplify the expression by dividing the numerator and denominator by -3: $t = \dfrac{-5y + 11}{6}$